Fitting INLA
forecast_date <- as.Date("2023-12-04")
d1 <- c1 %>%
filter(state == "TX", city %in% mycity,
collection_week >= "2021-07-01") %>%
mutate(city = factor(city, levels = mycity)) %>%
select(collection_week, state, city, influenza = influenza_7_day_sum)
hyper_epwk <- list(theta=list(prior="loggamma", param=c(1, 0.01))) # more favorable to large jumps
hyper_wk <- list(theta=list(prior="loggamma", param=c(1.5, 0.05))) # precision constrained away from 0; P(prec<1)=0.02%,
flu_model_shareseason_ar1_dist <- paste0(
'count ~ 1 + city + ',
'f(epiweek, model="rw2", cyclic=TRUE, hyper=hyper_epwk, scale.model=TRUE) + ',
'f(city_id, model="besagproper", graph=distance_matrix, hyper=hyper_wk, group=t, control.group=list(model="ar1"))'
)
flu_model_shareseason_ar1 <- flu_model_severalcity(epishare = TRUE, ar=1)
### exchangeable model
inla_fit_cities(d1 = d1, forecast_date = forecast_date, model = flu_model_shareseason_ar1,
mycity = mycity, hyper_epwk, hyper_wk, horizon = 4,
joint_season = TRUE, W.model = NULL, dist = FALSE)
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## $summary
## Time used:
## Pre = 1.5, Running = 2.3, Post = 0.102, Total = 3.89
## Fixed effects:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## (Intercept) 3.592 0.707 1.910 2.194 2.431 2.696
## citySAN ANTONIO -1.085 0.931 -3.299 -2.923 -2.611 -2.262
## cityDALLAS -0.919 0.933 -3.144 -2.767 -2.452 -2.101
## cityAUSTIN -1.186 0.933 -3.421 -3.040 -2.723 -2.369
## cityFORT WORTH -1.101 0.932 -3.316 -2.941 -2.629 -2.280
## cityEL PASO -0.601 0.931 -2.832 -2.451 -2.135 -1.782
## cityARLINGTON -2.083 0.935 -4.316 -3.936 -3.620 -3.268
## cityCORPUS CHRISTI -1.282 0.933 -3.523 -3.139 -2.821 -2.466
## cityPLANO -2.159 0.936 -4.399 -4.017 -3.700 -3.345
## cityLAREDO -4.571 0.972 -6.940 -6.530 -6.190 -5.811
## cityLUBBOCK -3.578 0.964 -5.921 -5.517 -5.181 -4.807
## cityIRVING -3.771 0.943 -6.006 -5.629 -5.315 -4.963
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## (Intercept) 2.872 3.009 3.126 3.230 3.327 3.418
## citySAN ANTONIO -2.032 -1.852 -1.698 -1.561 -1.435 -1.315
## cityDALLAS -1.869 -1.688 -1.534 -1.396 -1.269 -1.149
## cityAUSTIN -2.136 -1.954 -1.799 -1.661 -1.534 -1.413
## cityFORT WORTH -2.050 -1.869 -1.715 -1.578 -1.451 -1.331
## cityEL PASO -1.549 -1.368 -1.213 -1.075 -0.948 -0.828
## cityARLINGTON -3.035 -2.853 -2.698 -2.560 -2.433 -2.312
## cityCORPUS CHRISTI -2.232 -2.049 -1.894 -1.756 -1.628 -1.508
## cityPLANO -3.112 -2.929 -2.774 -2.635 -2.507 -2.387
## cityLAREDO -5.562 -5.368 -5.204 -5.058 -4.924 -4.798
## cityLUBBOCK -4.561 -4.369 -4.207 -4.063 -3.930 -3.805
## cityIRVING -4.731 -4.548 -4.393 -4.254 -4.126 -4.005
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## (Intercept) 3.506 3.592 3.679 3.767 3.858 3.954
## citySAN ANTONIO -1.199 -1.086 -0.972 -0.857 -0.737 -0.610
## cityDALLAS -1.033 -0.919 -0.805 -0.689 -0.569 -0.442
## cityAUSTIN -1.297 -1.183 -1.069 -0.954 -0.834 -0.707
## cityFORT WORTH -1.216 -1.102 -0.988 -0.872 -0.752 -0.626
## cityEL PASO -0.712 -0.599 -0.485 -0.369 -0.250 -0.123
## cityARLINGTON -2.196 -2.082 -1.967 -1.851 -1.731 -1.604
## cityCORPUS CHRISTI -1.392 -1.278 -1.164 -1.048 -0.929 -0.803
## cityPLANO -2.270 -2.156 -2.042 -1.925 -1.805 -1.678
## cityLAREDO -4.676 -4.557 -4.438 -4.318 -4.194 -4.064
## cityLUBBOCK -3.684 -3.566 -3.449 -3.329 -3.206 -3.077
## cityIRVING -3.888 -3.772 -3.657 -3.540 -3.418 -3.290
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant 0.975quant
## (Intercept) 4.059 4.175 4.313 4.488 4.753 4.989
## citySAN ANTONIO -0.473 -0.319 -0.138 0.093 0.444 0.757
## cityDALLAS -0.304 -0.150 0.031 0.262 0.612 0.925
## cityAUSTIN -0.570 -0.417 -0.237 -0.008 0.340 0.650
## cityFORT WORTH -0.488 -0.334 -0.152 0.079 0.430 0.744
## cityEL PASO 0.013 0.166 0.346 0.576 0.923 1.233
## cityARLINGTON -1.467 -1.312 -1.131 -0.900 -0.551 -0.238
## cityCORPUS CHRISTI -0.666 -0.513 -0.333 -0.105 0.241 0.549
## cityPLANO -1.541 -1.387 -1.206 -0.975 -0.626 -0.315
## cityLAREDO -3.923 -3.765 -3.582 -3.349 -2.999 -2.690
## cityLUBBOCK -2.937 -2.781 -2.598 -2.366 -2.018 -1.709
## cityIRVING -3.150 -2.994 -2.810 -2.576 -2.220 -1.902
## 0.99quant mode kld
## (Intercept) 5.273 3.592 0
## citySAN ANTONIO 1.134 -1.086 0
## cityDALLAS 1.301 -0.919 0
## cityAUSTIN 1.022 -1.183 0
## cityFORT WORTH 1.123 -1.102 0
## cityEL PASO 1.605 -0.599 0
## cityARLINGTON 0.138 -2.082 0
## cityCORPUS CHRISTI 0.920 -1.278 0
## cityPLANO 0.059 -2.156 0
## cityLAREDO -2.319 -4.557 0
## cityLUBBOCK -1.339 -3.566 0
## cityIRVING -1.519 -3.772 0
##
## Random effects:
## Name Model
## epiweek RW2 model
## t AR1 model
##
## Model hyperparameters:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## Precision for epiweek 4.121 3.042 0.840 1.035 1.239 1.530
## Precision for t 0.317 0.049 0.216 0.229 0.241 0.256
## Rho for t 0.911 0.014 0.874 0.881 0.886 0.892
## GroupRho for t 0.132 0.031 0.067 0.076 0.084 0.093
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## Precision for epiweek 1.763 1.976 2.183 2.391 2.602 2.820
## Precision for t 0.266 0.274 0.282 0.288 0.295 0.301
## Rho for t 0.896 0.899 0.902 0.904 0.906 0.908
## GroupRho for t 0.100 0.105 0.110 0.114 0.119 0.123
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## Precision for epiweek 3.049 3.298 3.573 3.881 4.229 4.627
## Precision for t 0.307 0.313 0.319 0.326 0.332 0.340
## Rho for t 0.910 0.912 0.914 0.915 0.917 0.919
## GroupRho for t 0.126 0.130 0.134 0.138 0.142 0.147
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant
## Precision for epiweek 5.104 5.707 6.511 7.682 9.837
## Precision for t 0.348 0.357 0.367 0.381 0.403
## Rho for t 0.921 0.923 0.925 0.928 0.932
## GroupRho for t 0.152 0.158 0.164 0.173 0.186
## 0.975quant 0.99quant mode
## Precision for epiweek 12.216 15.706 2.207
## Precision for t 0.423 0.447 0.307
## Rho for t 0.936 0.940 0.913
## GroupRho for t 0.198 0.212 0.126
##
## Deviance Information Criterion (DIC) ...............: 8090.56
## Deviance Information Criterion (DIC, saturated) ....: 2939.82
## Effective number of parameters .....................: 988.59
##
## Watanabe-Akaike information criterion (WAIC) ...: 8111.94
## Effective number of parameters .................: 742.02
##
## Marginal log-Likelihood: -5232.28
## is computed
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
##
##
## $wis
## # A tibble: 48 × 3
## collection_week city wis_mean
## <date> <fct> <dbl>
## 1 2023-12-10 HOUSTON 165.
## 2 2023-12-10 SAN ANTONIO 18.2
## 3 2023-12-10 DALLAS 88.6
## 4 2023-12-10 AUSTIN 11.7
## 5 2023-12-10 FORT WORTH 55.9
## 6 2023-12-10 EL PASO 105.
## 7 2023-12-10 ARLINGTON 15.4
## 8 2023-12-10 CORPUS CHRISTI 3.08
## 9 2023-12-10 PLANO 7.65
## 10 2023-12-10 LAREDO 0.425
## # ℹ 38 more rows
### add distance
inla_fit_cities(d1 = d1, forecast_date = forecast_date, model = flu_model_shareseason_ar1_dist,
mycity = mycity, hyper_epwk, hyper_wk, horizon = 4,
joint_season = TRUE, W.model = NULL, dist = TRUE)
## $summary
## Time used:
## Pre = 1.41, Running = 2.46, Post = 0.0821, Total = 3.95
## Fixed effects:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## (Intercept) 3.586 0.682 1.969 2.240 2.467 2.721
## citySAN ANTONIO -1.088 0.878 -3.172 -2.821 -2.529 -2.201
## cityDALLAS -0.923 0.881 -3.019 -2.666 -2.371 -2.041
## cityAUSTIN -1.184 0.881 -3.288 -2.931 -2.634 -2.302
## cityFORT WORTH -1.106 0.880 -3.193 -2.842 -2.549 -2.221
## cityEL PASO -0.596 0.879 -2.695 -2.340 -2.044 -1.712
## cityARLINGTON -2.072 0.883 -4.173 -3.819 -3.523 -3.192
## cityCORPUS CHRISTI -1.274 0.880 -3.382 -3.023 -2.725 -2.392
## cityPLANO -2.163 0.884 -4.273 -3.916 -3.618 -3.285
## cityLAREDO -4.603 0.921 -6.846 -6.459 -6.138 -5.780
## cityLUBBOCK -3.545 0.911 -5.755 -5.376 -5.060 -4.708
## cityIRVING -3.807 0.891 -5.917 -5.564 -5.268 -4.936
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## (Intercept) 2.890 3.022 3.135 3.236 3.329 3.417
## citySAN ANTONIO -1.984 -1.813 -1.668 -1.538 -1.419 -1.305
## cityDALLAS -1.822 -1.650 -1.504 -1.374 -1.254 -1.140
## cityAUSTIN -2.082 -1.910 -1.764 -1.633 -1.513 -1.399
## cityFORT WORTH -2.004 -1.833 -1.688 -1.558 -1.438 -1.324
## cityEL PASO -1.493 -1.321 -1.175 -1.045 -0.925 -0.811
## cityARLINGTON -2.973 -2.801 -2.655 -2.524 -2.404 -2.290
## cityCORPUS CHRISTI -2.172 -1.999 -1.853 -1.722 -1.601 -1.487
## cityPLANO -3.065 -2.892 -2.745 -2.614 -2.493 -2.379
## cityLAREDO -5.544 -5.360 -5.204 -5.065 -4.938 -4.818
## cityLUBBOCK -4.476 -4.295 -4.141 -4.004 -3.878 -3.759
## cityIRVING -4.717 -4.544 -4.397 -4.265 -4.144 -4.029
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## (Intercept) 3.502 3.586 3.670 3.755 3.843 3.936
## citySAN ANTONIO -1.196 -1.088 -0.981 -0.871 -0.758 -0.638
## cityDALLAS -1.030 -0.922 -0.814 -0.704 -0.591 -0.470
## cityAUSTIN -1.289 -1.181 -1.073 -0.963 -0.850 -0.730
## cityFORT WORTH -1.215 -1.107 -0.999 -0.890 -0.776 -0.656
## cityEL PASO -0.702 -0.594 -0.486 -0.377 -0.263 -0.144
## cityARLINGTON -2.180 -2.071 -1.963 -1.853 -1.739 -1.619
## cityCORPUS CHRISTI -1.378 -1.270 -1.162 -1.052 -0.939 -0.820
## cityPLANO -2.269 -2.160 -2.052 -1.942 -1.828 -1.708
## cityLAREDO -4.702 -4.589 -4.476 -4.362 -4.244 -4.120
## cityLUBBOCK -3.645 -3.533 -3.422 -3.308 -3.192 -3.069
## cityIRVING -3.917 -3.808 -3.699 -3.588 -3.472 -3.351
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant 0.975quant
## (Intercept) 4.037 4.150 4.283 4.452 4.707 4.934
## citySAN ANTONIO -0.508 -0.363 -0.192 0.026 0.355 0.649
## cityDALLAS -0.340 -0.195 -0.024 0.194 0.523 0.816
## cityAUSTIN -0.601 -0.456 -0.286 -0.069 0.258 0.548
## cityFORT WORTH -0.526 -0.380 -0.209 0.009 0.339 0.633
## cityEL PASO -0.014 0.130 0.300 0.517 0.843 1.133
## cityARLINGTON -1.489 -1.343 -1.172 -0.954 -0.624 -0.331
## cityCORPUS CHRISTI -0.690 -0.546 -0.376 -0.160 0.165 0.454
## cityPLANO -1.578 -1.432 -1.261 -1.044 -0.716 -0.424
## cityLAREDO -3.987 -3.838 -3.664 -3.445 -3.116 -2.825
## cityLUBBOCK -2.936 -2.788 -2.615 -2.397 -2.068 -1.778
## cityIRVING -3.219 -3.071 -2.898 -2.677 -2.342 -2.045
## 0.99quant mode kld
## (Intercept) 5.206 3.586 0
## citySAN ANTONIO 1.001 -1.088 0
## cityDALLAS 1.167 -0.922 0
## cityAUSTIN 0.896 -1.181 0
## cityFORT WORTH 0.987 -1.107 0
## cityEL PASO 1.482 -0.594 0
## cityARLINGTON 0.021 -2.071 0
## cityCORPUS CHRISTI 0.801 -1.270 0
## cityPLANO -0.074 -2.160 0
## cityLAREDO -2.480 -4.589 0
## cityLUBBOCK -1.432 -3.533 0
## cityIRVING -1.687 -3.808 0
##
## Random effects:
## Name Model
## epiweek RW2 model
## city_id Proper version of Besags ICAR model
##
## Model hyperparameters:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## Precision for epiweek 3.901 1.794 1.373 1.587 1.798 2.080
## Precision for city_id 0.023 0.004 0.015 0.016 0.017 0.018
## Diagonal for city_id 5.053 1.074 3.018 3.263 3.489 3.768
## GroupRho for city_id 0.907 0.014 0.870 0.877 0.883 0.889
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## Precision for epiweek 2.294 2.481 2.657 2.827 2.996 3.165
## Precision for city_id 0.019 0.019 0.020 0.021 0.021 0.022
## Diagonal for city_id 3.971 4.138 4.286 4.424 4.558 4.688
## GroupRho for city_id 0.893 0.896 0.898 0.900 0.902 0.904
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## Precision for epiweek 3.338 3.520 3.716 3.929 4.164 4.426
## Precision for city_id 0.022 0.023 0.023 0.024 0.024 0.025
## Diagonal for city_id 4.816 4.945 5.076 5.215 5.363 5.524
## GroupRho for city_id 0.906 0.908 0.910 0.911 0.913 0.915
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant
## Precision for epiweek 4.727 5.094 5.564 6.217 7.332
## Precision for city_id 0.026 0.027 0.028 0.029 0.031
## Diagonal for city_id 5.701 5.904 6.151 6.478 6.993
## GroupRho for city_id 0.917 0.919 0.922 0.925 0.929
## 0.975quant 0.99quant mode
## Precision for epiweek 8.475 10.019 2.881
## Precision for city_id 0.033 0.035 0.022
## Diagonal for city_id 7.471 8.073 4.736
## GroupRho for city_id 0.932 0.936 0.909
##
## Deviance Information Criterion (DIC) ...............: 8120.05
## Deviance Information Criterion (DIC, saturated) ....: 2969.30
## Effective number of parameters .....................: 995.06
##
## Watanabe-Akaike information criterion (WAIC) ...: 8143.54
## Effective number of parameters .................: 748.11
##
## Marginal log-Likelihood: -5234.76
## is computed
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
##
##
## $wis
## # A tibble: 48 × 3
## collection_week city wis_mean
## <date> <fct> <dbl>
## 1 2023-12-10 HOUSTON 167.
## 2 2023-12-10 SAN ANTONIO 18.3
## 3 2023-12-10 DALLAS 90.3
## 4 2023-12-10 AUSTIN 11.7
## 5 2023-12-10 FORT WORTH 56.6
## 6 2023-12-10 EL PASO 105.
## 7 2023-12-10 ARLINGTON 15.6
## 8 2023-12-10 CORPUS CHRISTI 3.12
## 9 2023-12-10 PLANO 7.70
## 10 2023-12-10 LAREDO 0.434
## # ℹ 38 more rows
################################
#### fitting INLA with several dates
################################
### exchangeable model
inla_fit_several_forecastdate_cities(d1, forecast_date = c("2023-10-01", "2023-11-19", "2024-01-07", "2024-02-18", "2024-03-24"),
model = flu_model_shareseason_ar1, mycity = mycity, hyper_epwk = hyper_epwk, hyper_wk = hyper_wk, horizon = 4,
joint_season = TRUE, W.model = "ar1, share seaseon, exchangeable")
## $summary
## Time used:
## Pre = 1.35, Running = 2.21, Post = 0.0924, Total = 3.65
## Fixed effects:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## (Intercept) 3.703 0.702 2.019 2.309 2.548 2.815
## citySAN ANTONIO -1.029 0.916 -3.211 -2.837 -2.528 -2.184
## cityDALLAS -0.760 0.918 -2.954 -2.577 -2.266 -1.919
## cityAUSTIN -1.132 0.918 -3.333 -2.953 -2.640 -2.292
## cityFORT WORTH -0.836 0.917 -3.014 -2.642 -2.335 -1.992
## cityEL PASO -0.603 0.917 -2.802 -2.422 -2.109 -1.761
## cityARLINGTON -1.896 0.920 -4.092 -3.715 -3.403 -3.057
## cityCORPUS CHRISTI -1.392 0.918 -3.593 -3.213 -2.899 -2.551
## cityPLANO -1.924 0.921 -4.124 -3.746 -3.433 -3.086
## cityLAREDO -3.950 0.943 -6.226 -5.831 -5.506 -5.145
## cityLUBBOCK -3.035 0.940 -5.309 -4.914 -4.588 -4.227
## cityIRVING -3.585 0.925 -5.786 -5.410 -5.099 -4.752
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## (Intercept) 2.990 3.127 3.243 3.347 3.442 3.532
## citySAN ANTONIO -1.958 -1.781 -1.631 -1.496 -1.372 -1.255
## cityDALLAS -1.692 -1.514 -1.363 -1.228 -1.103 -0.986
## cityAUSTIN -2.064 -1.885 -1.733 -1.598 -1.474 -1.356
## cityFORT WORTH -1.767 -1.590 -1.440 -1.306 -1.182 -1.064
## cityEL PASO -1.533 -1.354 -1.203 -1.068 -0.943 -0.826
## cityARLINGTON -2.829 -2.651 -2.499 -2.364 -2.240 -2.122
## cityCORPUS CHRISTI -2.323 -2.144 -1.992 -1.857 -1.733 -1.615
## cityPLANO -2.858 -2.679 -2.528 -2.392 -2.268 -2.150
## cityLAREDO -4.908 -4.723 -4.566 -4.426 -4.298 -4.176
## cityLUBBOCK -3.990 -3.805 -3.648 -3.509 -3.381 -3.260
## cityIRVING -4.524 -4.345 -4.193 -4.057 -3.932 -3.814
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## (Intercept) 3.619 3.705 3.790 3.877 3.967 4.062
## citySAN ANTONIO -1.142 -1.031 -0.919 -0.806 -0.688 -0.564
## cityDALLAS -0.872 -0.760 -0.649 -0.535 -0.417 -0.293
## cityAUSTIN -1.242 -1.131 -1.019 -0.906 -0.788 -0.664
## cityFORT WORTH -0.951 -0.840 -0.728 -0.615 -0.497 -0.372
## cityEL PASO -0.712 -0.601 -0.489 -0.376 -0.259 -0.135
## cityARLINGTON -2.008 -1.896 -1.784 -1.670 -1.552 -1.428
## cityCORPUS CHRISTI -1.501 -1.390 -1.278 -1.165 -1.048 -0.924
## cityPLANO -2.036 -1.924 -1.812 -1.698 -1.580 -1.455
## cityLAREDO -4.059 -3.945 -3.830 -3.714 -3.593 -3.466
## cityLUBBOCK -3.143 -3.029 -2.914 -2.798 -2.678 -2.552
## cityIRVING -3.699 -3.587 -3.474 -3.359 -3.241 -3.115
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant 0.975quant
## (Intercept) 4.165 4.280 4.415 4.588 4.850 5.084
## citySAN ANTONIO -0.429 -0.277 -0.099 0.129 0.477 0.790
## cityDALLAS -0.158 -0.007 0.172 0.400 0.746 1.058
## cityAUSTIN -0.529 -0.378 -0.201 0.026 0.371 0.681
## cityFORT WORTH -0.237 -0.085 0.095 0.324 0.674 0.989
## cityEL PASO 0.000 0.150 0.327 0.554 0.898 1.207
## cityARLINGTON -1.292 -1.141 -0.962 -0.734 -0.386 -0.073
## cityCORPUS CHRISTI -0.789 -0.638 -0.461 -0.234 0.110 0.419
## cityPLANO -1.320 -1.168 -0.990 -0.761 -0.414 -0.101
## cityLAREDO -3.329 -3.175 -2.994 -2.763 -2.414 -2.102
## cityLUBBOCK -2.415 -2.262 -2.082 -1.852 -1.505 -1.195
## cityIRVING -2.978 -2.825 -2.645 -2.414 -2.063 -1.747
## 0.99quant mode kld
## (Intercept) 5.368 3.705 0
## citySAN ANTONIO 1.170 -1.030 0
## cityDALLAS 1.436 -0.760 0
## cityAUSTIN 1.057 -1.131 0
## cityFORT WORTH 1.372 -0.840 0
## cityEL PASO 1.582 -0.601 0
## cityARLINGTON 0.306 -1.896 0
## cityCORPUS CHRISTI 0.794 -1.390 0
## cityPLANO 0.277 -1.924 0
## cityLAREDO -1.724 -3.945 0
## cityLUBBOCK -0.819 -3.029 0
## cityIRVING -1.364 -3.587 0
##
## Random effects:
## Name Model
## epiweek RW2 model
## t AR1 model
##
## Model hyperparameters:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## Precision for epiweek 3.214 2.181 0.645 0.806 0.975 1.216
## Precision for t 0.345 0.056 0.229 0.244 0.258 0.275
## Rho for t 0.928 0.012 0.896 0.902 0.907 0.912
## GroupRho for t 0.149 0.028 0.089 0.097 0.105 0.114
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## Precision for epiweek 1.412 1.590 1.759 1.927 2.100 2.277
## Precision for t 0.287 0.297 0.305 0.313 0.320 0.328
## Rho for t 0.915 0.918 0.920 0.922 0.924 0.925
## GroupRho for t 0.120 0.125 0.129 0.133 0.137 0.141
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## Precision for epiweek 2.462 2.657 2.868 3.103 3.369 3.673
## Precision for t 0.335 0.342 0.349 0.356 0.364 0.372
## Rho for t 0.927 0.928 0.930 0.931 0.933 0.935
## GroupRho for t 0.144 0.148 0.151 0.155 0.159 0.163
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant
## Precision for epiweek 4.028 4.463 5.036 5.869 7.352
## Precision for t 0.381 0.391 0.403 0.419 0.443
## Rho for t 0.936 0.938 0.940 0.943 0.946
## GroupRho for t 0.167 0.172 0.178 0.186 0.197
## 0.975quant 0.99quant mode
## Precision for epiweek 8.944 11.240 1.827
## Precision for t 0.465 0.491 0.337
## Rho for t 0.949 0.953 0.929
## GroupRho for t 0.207 0.219 0.146
##
## Deviance Information Criterion (DIC) ...............: 9729.35
## Deviance Information Criterion (DIC, saturated) ....: 3387.62
## Effective number of parameters .....................: 1108.42
##
## Watanabe-Akaike information criterion (WAIC) ...: 9758.02
## Effective number of parameters .................: 840.75
##
## Marginal log-Likelihood: -6223.80
## is computed
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
##
##
## $wis
## # A tibble: 240 × 3
## collection_week city wis_mean
## <date> <fct> <dbl>
## 1 2023-10-01 HOUSTON 13.9
## 2 2023-10-01 SAN ANTONIO 12.5
## 3 2023-10-01 DALLAS 7.25
## 4 2023-10-01 AUSTIN 10.3
## 5 2023-10-01 FORT WORTH 7.53
## 6 2023-10-01 EL PASO 8.94
## 7 2023-10-01 ARLINGTON 8.42
## 8 2023-10-01 CORPUS CHRISTI 2.66
## 9 2023-10-01 PLANO 1.30
## 10 2023-10-01 LAREDO 0.394
## # ℹ 230 more rows
### add distance
inla_fit_several_forecastdate_cities(d1, forecast_date = c("2023-10-01", "2023-11-19", "2024-01-07", "2024-02-18", "2024-03-24"),
model = flu_model_shareseason_ar1_dist, mycity = mycity, hyper_epwk = hyper_epwk, hyper_wk = hyper_wk, horizon = 4,
joint_season = TRUE, W.model = "ar1, share seaseon, dist", dist = TRUE)
## $summary
## Time used:
## Pre = 1.68, Running = 2.76, Post = 0.0952, Total = 4.54
## Fixed effects:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## (Intercept) 3.698 0.685 2.058 2.337 2.569 2.829
## citySAN ANTONIO -1.033 0.878 -3.118 -2.764 -2.470 -2.142
## cityDALLAS -0.766 0.880 -2.861 -2.505 -2.209 -1.878
## cityAUSTIN -1.135 0.880 -3.236 -2.877 -2.580 -2.248
## cityFORT WORTH -0.844 0.879 -2.926 -2.574 -2.281 -1.954
## cityEL PASO -0.602 0.878 -2.702 -2.343 -2.046 -1.714
## cityARLINGTON -1.890 0.881 -3.989 -3.632 -3.336 -3.005
## cityCORPUS CHRISTI -1.391 0.879 -3.493 -3.134 -2.836 -2.504
## cityPLANO -1.932 0.882 -4.034 -3.676 -3.379 -3.048
## cityLAREDO -3.986 0.904 -6.167 -5.792 -5.481 -5.135
## cityLUBBOCK -3.026 0.901 -5.198 -4.825 -4.516 -4.170
## cityIRVING -3.609 0.887 -5.715 -5.358 -5.062 -4.730
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## (Intercept) 3.000 3.134 3.247 3.349 3.442 3.531
## citySAN ANTONIO -1.925 -1.756 -1.611 -1.482 -1.363 -1.250
## cityDALLAS -1.660 -1.490 -1.344 -1.215 -1.095 -0.982
## cityAUSTIN -2.029 -1.858 -1.712 -1.583 -1.463 -1.350
## cityFORT WORTH -1.738 -1.568 -1.424 -1.295 -1.176 -1.063
## cityEL PASO -1.495 -1.324 -1.179 -1.049 -0.930 -0.817
## cityARLINGTON -2.787 -2.616 -2.470 -2.341 -2.221 -2.108
## cityCORPUS CHRISTI -2.285 -2.114 -1.968 -1.839 -1.719 -1.606
## cityPLANO -2.829 -2.658 -2.512 -2.382 -2.262 -2.149
## cityLAREDO -4.907 -4.729 -4.578 -4.443 -4.320 -4.203
## cityLUBBOCK -3.944 -3.766 -3.616 -3.482 -3.358 -3.242
## cityIRVING -4.511 -4.340 -4.193 -4.063 -3.942 -3.828
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## (Intercept) 3.616 3.700 3.783 3.868 3.957 4.049
## citySAN ANTONIO -1.142 -1.035 -0.927 -0.818 -0.705 -0.586
## cityDALLAS -0.873 -0.766 -0.658 -0.549 -0.436 -0.317
## cityAUSTIN -1.241 -1.133 -1.026 -0.917 -0.804 -0.685
## cityFORT WORTH -0.954 -0.847 -0.740 -0.631 -0.517 -0.398
## cityEL PASO -0.708 -0.601 -0.493 -0.385 -0.272 -0.153
## cityARLINGTON -1.998 -1.891 -1.783 -1.674 -1.560 -1.441
## cityCORPUS CHRISTI -1.497 -1.390 -1.282 -1.173 -1.061 -0.941
## cityPLANO -2.039 -1.932 -1.824 -1.715 -1.601 -1.481
## cityLAREDO -4.090 -3.979 -3.869 -3.757 -3.641 -3.519
## cityLUBBOCK -3.129 -3.019 -2.909 -2.798 -2.682 -2.561
## cityIRVING -3.718 -3.610 -3.502 -3.392 -3.277 -3.157
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant 0.975quant
## (Intercept) 4.150 4.263 4.395 4.564 4.819 5.047
## citySAN ANTONIO -0.456 -0.311 -0.140 0.078 0.410 0.707
## cityDALLAS -0.187 -0.042 0.129 0.347 0.678 0.975
## cityAUSTIN -0.555 -0.411 -0.240 -0.023 0.307 0.601
## cityFORT WORTH -0.268 -0.122 0.050 0.269 0.603 0.902
## cityEL PASO -0.024 0.121 0.291 0.508 0.836 1.130
## cityARLINGTON -1.311 -1.165 -0.994 -0.775 -0.443 -0.146
## cityCORPUS CHRISTI -0.812 -0.667 -0.497 -0.280 0.048 0.342
## cityPLANO -1.351 -1.206 -1.035 -0.816 -0.485 -0.188
## cityLAREDO -3.387 -3.239 -3.066 -2.846 -2.513 -2.217
## cityLUBBOCK -2.429 -2.282 -2.109 -1.890 -1.558 -1.263
## cityIRVING -3.026 -2.879 -2.706 -2.485 -2.151 -1.851
## 0.99quant mode kld
## (Intercept) 5.321 3.700 0
## citySAN ANTONIO 1.066 -1.034 0
## cityDALLAS 1.332 -0.766 0
## cityAUSTIN 0.956 -1.133 0
## cityFORT WORTH 1.262 -0.847 0
## cityEL PASO 1.484 -0.601 0
## cityARLINGTON 0.211 -1.891 0
## cityCORPUS CHRISTI 0.696 -1.390 0
## cityPLANO 0.169 -1.932 0
## cityLAREDO -1.862 -3.980 0
## cityLUBBOCK -0.907 -3.019 0
## cityIRVING -1.490 -3.610 0
##
## Random effects:
## Name Model
## epiweek RW2 model
## city_id Proper version of Besags ICAR model
##
## Model hyperparameters:
## mean sd 0.01quant 0.025quant 0.05quant 0.1quant
## Precision for epiweek 3.788 3.375 0.576 0.735 0.906 1.158
## Precision for city_id 0.026 0.005 0.016 0.018 0.019 0.020
## Diagonal for city_id 4.657 0.884 2.961 3.171 3.362 3.597
## GroupRho for city_id 0.924 0.012 0.894 0.899 0.904 0.909
## 0.15quant 0.2quant 0.25quant 0.3quant 0.35quant 0.4quant
## Precision for epiweek 1.366 1.559 1.750 1.945 2.145 2.355
## Precision for city_id 0.021 0.022 0.023 0.023 0.024 0.024
## Diagonal for city_id 3.766 3.905 4.028 4.143 4.253 4.360
## GroupRho for city_id 0.912 0.915 0.917 0.919 0.920 0.922
## 0.45quant 0.5quant 0.55quant 0.6quant 0.65quant 0.7quant
## Precision for epiweek 2.578 2.823 3.097 3.407 3.762 4.175
## Precision for city_id 0.025 0.026 0.026 0.027 0.027 0.028
## Diagonal for city_id 4.466 4.571 4.680 4.795 4.917 5.050
## GroupRho for city_id 0.923 0.925 0.926 0.928 0.929 0.931
## 0.75quant 0.8quant 0.85quant 0.9quant 0.95quant
## Precision for epiweek 4.674 5.315 6.187 7.486 9.949
## Precision for city_id 0.029 0.030 0.031 0.032 0.034
## Diagonal for city_id 5.195 5.361 5.564 5.832 6.250
## GroupRho for city_id 0.933 0.934 0.937 0.939 0.943
## 0.975quant 0.99quant mode
## Precision for epiweek 12.767 17.043 1.676
## Precision for city_id 0.036 0.038 0.025
## Diagonal for city_id 6.639 7.122 4.399
## GroupRho for city_id 0.946 0.949 0.926
##
## Deviance Information Criterion (DIC) ...............: 9754.45
## Deviance Information Criterion (DIC, saturated) ....: 3412.72
## Effective number of parameters .....................: 1114.26
##
## Watanabe-Akaike information criterion (WAIC) ...: 9782.25
## Effective number of parameters .................: 844.41
##
## Marginal log-Likelihood: -6225.40
## is computed
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
##
##
## $wis
## # A tibble: 240 × 3
## collection_week city wis_mean
## <date> <fct> <dbl>
## 1 2023-10-01 HOUSTON 14.2
## 2 2023-10-01 SAN ANTONIO 12.4
## 3 2023-10-01 DALLAS 7.04
## 4 2023-10-01 AUSTIN 10.3
## 5 2023-10-01 FORT WORTH 7.64
## 6 2023-10-01 EL PASO 8.75
## 7 2023-10-01 ARLINGTON 8.20
## 8 2023-10-01 CORPUS CHRISTI 2.69
## 9 2023-10-01 PLANO 1.35
## 10 2023-10-01 LAREDO 0.426
## # ℹ 230 more rows